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What program or application can calculate the value of Riemann zeta function for some s with large imaginary part (>10^19)? (How can one verify RH for large values?)

Rami Rami
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  • See also the comments from yesterday. – Dietrich Burde Dec 12 '19 at 11:59
  • find an algorithm than can compute Riemann Siegel well enough up to $10^{10^{500}}$ to get all the zeroes of the Hardy function there and one may have a chance to find missing zeroes to have an argument for the falsity of RH (though even missing zeroes can come from multiple zeroes of the Hardy function so that would still not disprove RH) - remmebering that so far the only way we now how to compute critical zeroes of RZ is using the Hardy function and finding enough sign changes for it – Conrad Dec 12 '19 at 13:21
  • It is way above your level to look at automated numerical checks of the RH for large $\Im(s)$, there are a lot of discussions on MSE about checking the RH for the first few non-trivial zeros. – reuns Dec 12 '19 at 15:04

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There are references given at Wikipedia, section Numerical calculations, using the Odlyzko–Schönhage algorithm. Andrew Odlyzko's homepage contains a lot of information about this. It appears that it is unlikely that we'll find a counterexample this way.

Dietrich Burde
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